Differential Equations: Student Projects

Last Updated November 3, 1996
The following projects were done by students in an introductory differential equations class. The instructions were to do an experiment related to first order differential equations and to present the results as a full lab report.

Note: These projects are shown in their raw, unedited form. Comments on each experiment will be provided at a leter date

Student Projects

Flow Rate as a Function of Orifice Diameter

• Authors: Ginger Hepler, Jeff Simon, and David Bednarczyk
• Abstract: The purpose of this experiment was to develop a differential equation to model the flow rate as a function of orifice diameter. The delivery system modeled was at a residential home. Our results fit the logistics equation. The carrying capacity was equal to the maximum flow rate of the system, which was estimated at 5.63 gallons per minute (GPM).
• Files: paper, data, Maple file.

Video Tape Counters: The Exponential Measure of Time

• Authors: Cordelia Galphin, Joseph Glembocki, and Jack Tompkins
• Abstract: When watching a movie on a video tape, people usually believe that the counter acts on a linear function of time. However, the counter actually behaves as an exponential function of time. As the reel gains tape, its radius increases. The velocity of the tape across the head is constant. Therefore, as the circumference of the reel increases proportionally to the increase of the radius, the angular velocity of the reel must decrease. After watching the tape twice, we graph the number on the tapecounter verse’s time. Through separable differential equations we are able to determine the equation for the relationship between the counter and time. Finally, we check the graph of the equation against the graph of our original data. Quantitative and qualitative analyses of these graphs reveal that our derived equations accruately portray the relationship between counter readings and time.
• Supplements: paper, data, Maple file.

Estimating Time of Death

• Authors: Tom Woodson, Clayton Tyndall, and Chris Stephenson
• Abstract:An experiment in estimating the time of death was performed where a potato was used instead of a human body. The time of death for the potato was considered to be the time it was taken out of the oven. The temperature of the potato at the time of death was 194F. Temperature readings of the potato were taken every fifteen minutes for three hours. Estimates for the time of death at the corresponding temperatures were calculated with an average percent error of 7.29%. The ambient temperature was 75.2F.
• Supplements: paper, data, AmiPro Version.

Alcohol Evaporation

• Authors: Ted Cook, Susan English, and Katie Lanier
• Abstract: The purpose of our experiment was to measure the rate of evaporation of anhydrous isopropyl alcohol. The experiment involved measuring the amount of alcohol that evaporated from a glass, funnel-shaped container every twelve hours. These values were then plotted and the resulting equation was found to be y=101.38e-.0026x.
• Supplements: paper, data.

Inversion of Sucrose: Kinetics of a Pseudo-First Order Reaction Determmined by Polarimetry.

• Authors: Bonnie Jenkins, Jennifer Williams
• Abstract: This is a simple experiment that demonstrates the decomposition of sucrose by dissolving sucrose in hydrochloric acid. The products formed are optically active and their optical rotation can be determined by use of a polarimeter. This first order reaction follows a differential equation.
• Supplements: paper, data.

Newton's Law of Cooling

• Authors: Alison Ford, Carly Bell, Toni Gurley, and Katie Faircloth
• Abstract: The purpose of this experiment is to determine if the cooling of water in different surroundings complies with the principles of Newton's Law of Cooling. The ambient temperatures will be that of room temperature (about 25 C) and of freezing temperatures (about 5 C). For each set of data, the cooling constant (k) was calculated from the slope of the plot of ln(T-Ta) vs time (sec). The k value at room temperature was 0.0002 sec^(-1) and at freezing temperature it was 0.0003 sec^(-1).
• Supplements: Not available yet.

Torricelli's Law: The Height of a Water Column

• Authors: Antonio J. Anderson, Travis Humble, Amanda J. Jorgeson-Litton, and E. A. Minga
• Abstract: In our experiment, we are attempting to find a relationship between the height of a column of water with constant cross-sectional area and time. In doing so, we found that the relation between these two variables, height and time, is quadratic in t.
• Supplements: Not available yet.
ions Course. The manual has been written to be